dolfin team mailing list archive

[Hatef Monajemi <hmonajem@xxxxxxxxxxxxxxxxxxx>]

Johan Hake wrote:
> On Wednesday 04 March 2009 08:21:11 Anders Logg wrote:
> > On Tue, Mar 03, 2009 at 08:08:56PM -0500, Hatef Monajemi wrote:
> > > Hi
> > >
> > > I was just wondering if it is possible to implement the 
Petrov-Galerkin
> > > type of weighting functions in dolfin. I am trying to solve a 
convection
> > > dominated problem in which the use of standard Galerkin weighting
> > > generates the oscillations which can be removed by upwinding. Is 
there
> > > any demo which shows the implementation of Petrov-Galerkin type of
> > > testfunctions.
> > >
> > > Thanks,
> > >
> > > Hatef
> >
> > Yes, look at
> >
> >   demo/pde/stokes/stabilized
> >
> > It's very straightforward, just write
> >
> >   v = TestFunction(V)
> >   v = v + delta*A(v)
> >
> > where delta is a stabilization parameter and A is a suitable 
operator.

That works fine when you have one Testfunction like "v", How about when 
you have the following set of Testfunction:
-->
P2 = VectorElement("Lagrange", "triangle", 1)
P1 = FiniteElement("Lagrange", "triangle", 1)
TH = P2 + P1

(v,w) = TestFunctions(TH)
-->

The analogy with what anders said, one should be able to do something 
like :

(v,w)=( v + delta*A(v), w) 

However, this creates problem in ffc. An alternative is to multiply the 
whole equation sets by the added stabilization term "delta*A(v)" and 
add the new terms to the unstabilized variational form. But it is much 
easier if one can just change the weighing functions v to v+delta*A(v). 
is there anyway to do that?

 
> The stabilizing parameter showed in this demo is quite crude. If it 
wont work 
> for you, you can consider:
> 
>   P = FunctionSpace(mesh,"CG",1)
>   V = VectorFunctionSpace(mesh,"CG"2)
>   v = TestFunction(P)
> 
>   field = Function(V,"Some vector valued function that drives the 
advection") 
>   stab = Function(V,open("SUPG_stab.h").read()) # V is a Vector
>   stab.field = field
> 
>   
>   v = v + 0.2*dot(stab,grad(v))
> 
> Here 0.2*stab relates to the delta Anders mention and A relates to grad
> 
> We could consider adding the handed function as a SpecialFunction in 
DOLFIN. 
> It is a general SUPG stabilization term, which depends not only on the 
local 
> meshsize but also on the local field size.
> 
> 
> Johan

Dear Johan:

Thanks for the better wight functions. I think these weight functions 
are those first introduced by Hughes and Brooks and also Kelly. Just 
one question? where in the element do you calculate your field 
variable? this method somehow assumes that field variable (velocity in 
my case) is constant over an element.

Hatef  


> 
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                   Message Attached :SUPG_stab.h
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                Message Attached :attached

--------------------------------------
Hatef Monajemi
Graduate Student
Dept of Civil and Environmental Eng
2032 MC Building, Carleton University 
1125 Colonel By Drive, Ottawa 
Ontario, Canada, K1S 5B6